On this page
Compound interest is interest earned on both the original principal and the accumulated interest from previous periods. It's exponential growth, and it's the primary engine of long-term wealth building.
Simple Interest vs. Compound Interest
Simple interest: Interest is only paid on the original principal.
Example: $10,000 at 5% simple interest
- Year 1 interest: $500 (5% of $10,000)
- Year 2 interest: $500 (5% of $10,000—same as year 1)
- Year 3 interest: $500 (5% of $10,000—same as year 1)
After 10 years: $10,000 + ($500 × 10) = $15,000
Compound interest: Interest is paid on principal plus accumulated interest.
Example: $10,000 at 5% compound interest (annual compounding)
- Year 1 interest: $500 (5% of $10,000)
- Year 1 balance: $10,500
- Year 2 interest: $525 (5% of $10,500)
- Year 2 balance: $11,025
- Year 3 interest: $551.25 (5% of $11,025)
- Year 3 balance: $11,576.25
After 10 years: $16,288.95 (compared to $15,000 with simple interest)
The difference is $1,288.95—pure gain from compounding.
Exponential vs. Linear Growth
Simple interest grows linearly (straight line). Compound interest grows exponentially (curve).
50-year comparison at 5% annual return:
Simple interest: $10,000 + ($500 × 50) = $35,000 (linear growth)
Compound interest: $10,000 grows to $114,674 (exponential growth)
The compound interest account has 3.28x more money from the exact same rate applied over the same time period. The difference is compounding.
The Rule of 72
To estimate how long it takes money to double:
Rule of 72: Divide 72 by the annual return percentage
At 5% return: 72 ÷ 5 = 14.4 years to double
At 10% return: 72 ÷ 10 = 7.2 years to double
At 15% return: 72 ÷ 15 = 4.8 years to double
This is remarkably accurate. $10,000 at 10% annual return:
- 7 years: $19,487
- 14 years: $37,975 (roughly doubled twice)
- 21 years: $76,050 (roughly doubled three times)
Small return differences create massive long-term differences.
Starting Early: The Compounding Effect
Scenario: Retirement savings starting at different ages
Person A: Invests $5,000/year from age 25-35 (10 years), then stops
- Total invested: $50,000
- At 8% annual return by age 65: $871,000
Person B: Invests $5,000/year from age 35-65 (30 years)
- Total invested: $150,000
- At 8% annual return by age 65: $915,000
Person A invested only 1/3 the money but retired with nearly the same amount because their money had 30 extra years to compound.
Person C: Invests $5,000/year from age 25-65 (40 years)
- Total invested: $200,000
- At 8% annual return by age 65: $3,119,000
Starting 10 years earlier resulted in 3.5x more wealth.
Compounding Frequency
The more frequently interest compounds, the higher the final result:
$10,000 at 5% for 10 years:
Annual compounding: $16,288.95 Quarterly compounding: $16,453.09 Monthly compounding: $16,470.09 Daily compounding: $16,486.65 Continuous compounding: $16,487.21
The difference between annual and continuous is $198.26—small in absolute terms, but the principle is clear: more frequent compounding = higher returns.
This is why savings accounts specify compounding frequency. Daily compounding outperforms monthly compounding.
Compounding and Inflation
Compound interest must exceed inflation to create real wealth:
Scenario: $10,000 investment, 2% inflation
At 2% returns: Real return = 0% (no purchasing power increase) At 5% returns: Real return = 3% (real wealth grows) At 10% returns: Real return = 8% (significant wealth growth)
This is why stocks (returning ~10%) beat bonds (~5%) beat savings accounts (~0.5%) over long periods. The extra 5% compounds into massive real wealth differences.
Debt Compounding (Negative)
Compounding works against borrowers too:
$5,000 credit card debt at 18% APR
- Year 1 interest: $900
- Year 2 interest: $1,063.20 (interest on the growing balance)
- Year 3 interest: $1,254.73 (growing further)
If you only pay interest and never pay principal, debt never decreases. If you pay slowly, compound interest makes the debt balloon.
This is why paying down high-interest debt quickly is critical—you're fighting compound interest working against you.
The Wealth-Building Implications
1. Time is your most valuable asset: A young person with $5,000 and 40 years to invest will often be wealthier than an older person with $50,000 and 5 years to invest.
2. Small percentage differences matter: 5% vs. 7% annual return seems like 2 percentage points. Over 40 years, it's the difference between $460,000 and $1,020,000 (2.2x difference).
3. Starting small is better than waiting: $50/month starting at 25 beats $500/month starting at 35. Time compounds wealth more than contribution size.
4. Consistency matters: $5,000/year every year compounds better than $50,000 once because you're capturing returns on intermediate balances.
The Bottom Line
Compound interest is the secret to wealth building. Warren Buffett became a multibillionaire primarily through compound investment returns over 60+ years. Albert Einstein allegedly called it "the eighth wonder of the world."
The formula is simple: start early, invest consistently, minimize costs (fees eat into compounding), and let time do the heavy lifting. Compound interest doesn't care if you're wealthy—it works for anyone who invests long-term.
